Pulsed Doppler ultrasound systems are commonly used to measure and map the velocity of blood flow within human and animal bodies. Pulses of ultrasound energy are directed into the body along a path which intersects blood vessels or a coronary chamber. Ultrasound energy from the pulses is backscattered from blood within the vessel or chamber and returns to a transducer where it is converted into an electrical signal. If the blood has a velocity component along the direction of propagation of the ultrasound waves, the frequency of the scattered echoes will be shifted, in relation to the frequency of the incident ultrasound energy. The Doppler shift which is thus induced in the echoes can be analyzed to yield a numeric estimate of the blood velocity and/or to produce a map of blood velocity as a function of position within the body.
U.S. Pat. 4,930,513 describes a system wherein the amplitude of echoes along an ultrasound A-line are sampled at discrete times at a rate which is above the Nyquist frequency. RF sample vectors at a selected range from successive A-lines, taken in the same direction through a region of the body, form a two-dimensional matrix with element positions described by a first, fast-time, variable which specifies the range of a data sample along its A-line, and a second, slow-time, variable which specifies the position of the A-line within a group of collected A-lines. The data matrix is processed with a two-dimensional discrete Fourier transform, taken with respect to the fast-time variable and the slow-time variable, which maps the data set into a discrete two-dimensional Fourier frequency space wherein constant velocity Doppler shifts appear on radial lines whose angle with respect to the vertical axis is a function of velocity. The slow-time axis corresponds to a slow-frequency (Doppler frequency) axis in the two-dimensional Fourier frequency space and the fast-time axis corresponds to a fast frequency (radio frequency) axis in the Fourier frequency space. Echoes of wideband pulses which are scattered from a moving target are mapped as generally elliptical shapes in the two-dimensional Fourier space. The angle between the major axis of an ellipse and the coordinate axes is a high quality measure of the velocity of the scattering medium. The angular distribution of the spectrum in two-dimensional Fourier frequency space (and hence velocity components in the region of the object) are estimated by computing a radial projection of the transformed data array.
The discrete Fourier transform is periodic in nature. As a result, the spectral components produced by high velocity scatterers will tend to "wrap around" unit cells in the Fourier frequency space. This is the familiar "aliasing" problem associated with a Fourier transform of any sampled signal. Thus, a typical radial projection of the two dimensional spectrum generated by pulse echoes from a moving medium will have a number of peaks at different velocities. The peak with the greatest maximum and least width generally corresponds to the true velocity spectrum of the scattering medium. The other peaks, which are alias terms, generally have smaller maxima and greater widths. Because of the random nature of ultrasound scattering from blood, an alias term may occasionally have a higher maximum or a narrower width than the true term. However, it is very unusual for an alias term to have both a higher maximum and a narrower width than the true term. Thus, a human observer of a plotted radial projection can almost always identify the term in the radial projection that corresponds to the true velocity spectrum of the scattering medium.